小世界网络营销
Network Marketing on a Small-World Network
摘要：
我们研究了一个动态的网络营销模型，在一个小世界网络结构人工构建类似的瓦特-斯托加茨网络模型。与传统营销不同的是，消费者在网络营销中还可以扮演制造商的销售代理人的角色，而这种角色的激励则是制造商提供的介绍费。当连线概率$α$从0增加到1时，网络从一维规则有向网络变为星形网络，在星形网络中，除了一个参与者之外，所有参与者都连接到一个消费者。产品的价格$p$和介绍费$r$作为自由参数，使厂商利润最大化。据观察，在$α=0$的最大化的利润是恒定的独立于网络的大小$N$，而在$α\neq 0$，它与$N$线性增加。这与小世界的转变是平行的。它还表明，虽然$p$的最佳值在$α$的宽范围内保持在几乎恒定的水平，而$r$的最佳值对网络结构的变化是敏感的。消费者剩余也被研究和讨论。
英文摘要：
We investigate a dynamic model of network marketing in a small-world network structure artificially constructed similarly to the Watts-Strogatz network model. Different from the traditional marketing, consumers can also play the role of the manufacturer's selling agents in network marketing, which is stimulated by the referral fee the manufacturer offers. As the wiring probability $α$ is increased from zero to unity, the network changes from the one-dimensional regular directed network to the star network where all but one player are connected to one consumer. The price $p$ of the product and the referral fee $r$ are used as free parameters to maximize the profit of the manufacturer. It is observed that at $α=0$ the maximized profit is constant independent of the network size $N$ while at $α\neq 0$, it increases linearly with $N$. This is in parallel to the small-world transition. It is also revealed that while the optimal value of $p$ stays at an almost constant level in a broad range of $α$, that of $r$ is sensitive to a change in the network structure. The consumer surplus is also studied and discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
